Find the zeros of the function. Enter the solutions from least to greatest. $h (x)=(-4x -3)(x -3)$ $\text{lesser }x = $
Solution: For any two expressions $A$ and $B$ : If $A\cdot B=0$ then either $A=0$ or $B=0$. This is called the zero product property. In our case, $(-4x -3)(x -3)=0$. So either $(-4x -3)=0$ or $(x -3)=0$ : $\begin{aligned} (1)&&-4x -3&=0 \\\\ &&-4x&=3 \\\\ &&x&=-\dfrac{3}{4} \end{aligned}$ $\begin{aligned} (2)&&x -3&=0 \\\\ &&x&=3 \end{aligned}$ In conclusion, $\begin{aligned} \text{lesser }x &= -\dfrac{3}{4} \\\\ \text{greater } x &= 3 \end{aligned}$